The Number Line · 3 min read
Scale and Real-World Models · Graphing Inequalities
A number line can use any scale, but the interval between consecutive marks must stay the same along the whole line. A line showing the integers from −10 to 10 has 21 evenly spaced marks, while a line from 0 to 1 might have a mark at every tenth (0, 0.1, 0.2, …, 1.0). Large numbers may be shown in intervals of 10, 100, or 1,000; small numbers in intervals of 0.1, 0.01, or 1/4.
| Situation | PositiveValues | NegativeValues |
|---|---|---|
| Temperature | Degreesabovezero | Degreesbelowzero |
| Elevation | Heightsabovesealevel | Depthsbelowsealevel |
| Money | Depositsandearnings;abalanceincreasestothe | Withdrawalsanddebts;abalancedecreasesto |
| right | theleft | |
| Time | Eventsafterachosenreferencepoint(zero) | Eventsbeforethereferencepoint |
An inequality can be graphed to show every number that satisfies it. An open circle means the endpoint is not included (< or >); a closed circle means the endpoint is included (≤ or ≥). To graph x > 3, place an open circle at 3 and shade to the right. To graph x ≤ −2, place a closed circle at −2 and shade to the left. A compound inequality such as −1 < x ≤ 4 has two conditions: an open circle at −1, a closed circle at 4, and shading between them.
Numbers increase to the right and decrease to the left.
Opposites are the same distance from zero; their sum is 0.
Of two negative numbers, the one closer to zero is greater:
Distance between two points is the absolute value of their
−2 > −5.
difference: from −4 to 2 is |2 − (−4)| = 6.
Absolute value is distance from zero and is never negative.
Open circle: < or >. Closed circle: ≤ or ≥.
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